【摘 要】
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Dynamics of three nonisospectral nonlinear Schr?dinger equations (NNLSEs), following different time dependencies of the spectral parameter, are investigated. Fi
【机 构】
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Department of Mathematics, Shanghai University, Shanghai 200444, China
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Dynamics of three nonisospectral nonlinear Schr?dinger equations (NNLSEs), following different time dependencies of the spectral parameter, are investigated. First, we discuss the gauge transformations between the standard nonlinear Schr?dinger equation (NLSE) and its first two nonisospectral counterparts, for which we derive solutions and infinitely many conserved quantities. Then, exact solutions of the three NNLSEs are derived in double Wronskian terms. Moreover, we analyze the dynamics of the solitons in the presence of the nonisospectral effects by demonstrating how the shapes, velocities, and wave energies change in time. In particular, we obtain a rogue wave type of soliton solutions to the third NNLSE.
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